Quantitative Neuroscience: From Chalk Board to Bedside

Abstract

Quantitative neuroscience, an interdisciplinary approach that brings together the mathematical, modeling, engineering and neuroscience communities, is rapidly bringing tangible hope of a better life to the tens of millions of people afflicted with diseases of the nervous system. The driving force is an increased understanding of how the nervous system exerts control and processes information. In less than 15 years, quantitative neuroscience is seemingly doing the impossible [12, 17]. Brain–computer interfaces now make it possible to translate thought into action [6, 7, 8, 15], replace lost limbs with robotic ones [9], prevent epileptic seizures [11, 16] and even to alleviate the symptoms of neuro–degenerative diseases, such as Parkinson’s [14]. Is it possible to do even better? The first theme of this issue explores two lines of mathematical research that have been particularly fruitful: 1) neural synchronization [19, 21], the fundamental process by which spatially distributed neural centers bind a sensory stimulus and coordinate their activities to respond to it, and 2) multistability [2, 10, 12], the concept that treatments may be possible by applying jolts of electricity to the right location in the brain at the right time [11, 16]. Attention is drawn to the effects of time delays and random perturbations (“noise”) on neural control and information processing. Since axonal conduction velocities are finite, time delays are an intrinsic component of all neural feedback loops. Stochastic effects arise from fluctuations in ion channels and quantal release and from the convergence of multiple independent synaptic inputs. Obviously the most promising mechanisms for neural processing are those which are robust in the presence of noise and delay. In other words, it is not only necessary to develop analytical expressions that describe neural synchronization regardless of the number of neurons [5], it is also necessary to understand the effects of noise of the dynamics of synchronizing neural populations [2]. Similarly the widespread occurrence of time–delayed feedback in neural pathways raises questions as to the role of time delays in information processing [10] and whether new effects arise from the interplay between noise